Two-stage optimal dispatching of multi-energy virtual power plants based on chance constraints and data-driven distributionally robust optimization considering carbon trading

Abstract

Multi-energy virtual power plant (MEVPP) has attracted more and more attention due to its advantages in renewable energy consumption and carbon emission reduction. However, the characteristics of multi-energy coupling and the access of renewable energy may lead to some challenges in the operation of MEVPP. In this paper, a data-driven distributionally robust chance constraints optimization model (DD-DRCCO) is proposed for the dispatching of MEVPP. Firstly, the uncertainties of wind power and photovoltaic output forecasting errors are modeled as an ambiguity set based on the Wasserstein metric. Secondly, combined with the chance constraint, the expected probability of the inequality constraint with uncertain variables is limited to the lowest allowable confidence level to improve the reliability of the model. Thirdly, the forecast errors of wind power and photovoltaic are considered in the constraint conditions, so that the system can effectively resist the interference of uncertain output. Besides, based on the strong duality theory, the DD-DRCCO model is equivalent to a MILP problem which is easy to solve. Finally, simulations implemented on a typical MEVPP are delivered to show that our proposed model: 1) The model is data-driven, and the conservativeness is kept at a low level, and the solution time is about 7s~8s; 2) The MEVPP system can achieve a balance between economy and low-carbon, making the total operation cost reduced by 0.89% compared with no increase of electric boiler; 3) The CO₂ emission during the operation of the MEVPP system was significantly reduced by about 87.33 kg.

Appendices

Appendix 1. Conditional value at risk approximation

The chance constraints in the model are nonlinear and difficult to solve directly. By introducing the relevant parameter vector α(x) and β(x), the chance constraints are simplified as follows:

$$\underset{\mathbb{P}\in \textbf{P}}{\operatorname{inf}}{E}_{\mathbb{P}}\left(\alpha (x)\cdot \overset{\sim }{\omega}\le \beta (x)\right)\ge 1-\tau$$

(37)

In this paper, the conditional risk value approximation of the above probability constraint formula is carried out by introducing auxiliary variables t₁, t₂, s_j, so as to convert it into a solvable linear constraint.

$$\underset{\mathbb{P}\in \textbf{P}}{\operatorname{inf}}{E}_{\mathbb{P}}\left(\alpha (x)\bullet \overset{\sim }{\omega}\le \beta (x)\right)\ge 1-\tau =\left\{\begin{array}{c}\boldsymbol{\upvarepsilon} {t}_1-\tau {t}_2\le \frac{1}{N}{\sum}_{j=1}^N{s}_j\\ {}{s}_j+{t}_2\le \max \left\{\beta (x)-\alpha (x){\overset{\sim }{\omega}}_j\right\}\\ {}{\left\Vert \alpha (x)\right\Vert}_{\ast}\le {t}_1\\ {}{t}_1\ge 0,{t}_2\ge 0,{s}_j\le 0\end{array}\right.$$

(38)

However, when the scale of the historical sample data is large, the number of auxiliary variables in the above formula will also increase, resulting in increased computational difficulty. Therefore， the above formula is further relaxed.

$$\underset{\mathbb{P}\in \textbf{P}}{\operatorname{inf}}{E}_{\mathbb{P}}\left(\alpha (x)\bullet \overset{\sim }{\omega}\le \beta (x)\right)\ge 1-\tau =\left\{\begin{array}{c}\boldsymbol{\upvarepsilon} {t}_1-\tau {t}_2\le \frac{1}{N}{\sum}_{j=1}^N\left\{\beta (x)-\alpha (x){\overset{\sim }{\omega}}_j-{t}_2\right\}\\ {}{\left\Vert \alpha (x)\right\Vert}_{\ast}\le {t}_1\\ {}{t}_1\ge 0,{t}_2\ge 0\end{array}\right.$$

(39)

Appendix 2. Relevant parameters

Table 3 Relevant parameters for MEVPP

Appendix 3. Hourly forecasted power data

Table 4 Photovoltaic output (kW)

Table 5 Wind power output (kW)